Some limit theorems for the critical Galton–Watson branching processes
UDC 519.21 We consider critical Galton–Watson processes starting from a random number of particles and determine the effect of the mean value of the initial state on the asymptotic state of the process. For processes starting from a large number of particles and satisfying the con...
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| Datum: | 2023 |
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Institute of Mathematics, NAS of Ukraine
2023
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512511012372480 |
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| author | Kudratov, Kh. Khusanbaev, Ya. Kudratov, Kh. Khusanbaev, Ya. |
| author_facet | Kudratov, Kh. Khusanbaev, Ya. Kudratov, Kh. Khusanbaev, Ya. |
| author_sort | Kudratov, Kh. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-05-14T15:30:08Z |
| description |
UDC 519.21
We consider critical Galton–Watson processes starting from a random number of particles and determine the effect of the mean value of the initial state on the asymptotic state of the process. For processes starting from a large number of particles and satisfying the condition $(S),$ we prove the limit theorem similar to the result of W. Feller. We also prove the theorem under the condition $W(n)>0$ for critical processes satisfying the conditions $(S)$ and $(M).$ |
| doi_str_mv | 10.37863/umzh.v75i4.6781 |
| first_indexed | 2026-03-24T03:29:57Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6781 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:57Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67812023-05-14T15:30:08Z Some limit theorems for the critical Galton–Watson branching processes Some limit theorems for the critical Galton–Watson branching processes Kudratov, Kh. Khusanbaev, Ya. Kudratov, Kh. Khusanbaev, Ya. Critical Galton-Watson process, generating function, slowly varying function. UDC 519.21 We consider critical Galton–Watson processes starting from a random number of particles and determine the effect of the mean value of the initial state on the asymptotic state of the process. For processes starting from a large number of particles and satisfying the condition $(S),$ we prove the limit theorem similar to the result of W. Feller. We also prove the theorem under the condition $W(n)>0$ for critical processes satisfying the conditions $(S)$ and $(M).$ УДК 519.21 Деякі граничні теореми для критичних розгалужених процесів Гальтона–Ватсона Розглянуто критичні процеси Гальтона–Ватсона, починаючи з випадкової кількості частинок, та визначено вплив середнього значення початкового стану на асимптотичний стан процесу. Для процесів, що починаються з великої кількості частинок і задовольняють умову $(S),$ доведено граничну теорему, подібну до результату В. Феллера. Також доведено теорему за умови, що $W(n)>0$ для критичних процесів, які задовольняють умови $(S)$ і $(M).$  Institute of Mathematics, NAS of Ukraine 2023-05-10 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6781 10.37863/umzh.v75i4.6781 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 4 (2023); 467 - 477 Український математичний журнал; Том 75 № 4 (2023); 467 - 477 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6781/9780 Copyright (c) 2023 Hamza Qudratov |
| spellingShingle | Kudratov, Kh. Khusanbaev, Ya. Kudratov, Kh. Khusanbaev, Ya. Some limit theorems for the critical Galton–Watson branching processes |
| title | Some limit theorems for the critical Galton–Watson branching processes |
| title_alt | Some limit theorems for the critical Galton–Watson branching processes |
| title_full | Some limit theorems for the critical Galton–Watson branching processes |
| title_fullStr | Some limit theorems for the critical Galton–Watson branching processes |
| title_full_unstemmed | Some limit theorems for the critical Galton–Watson branching processes |
| title_short | Some limit theorems for the critical Galton–Watson branching processes |
| title_sort | some limit theorems for the critical galton–watson branching processes |
| topic_facet | Critical Galton-Watson process generating function slowly varying function. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6781 |
| work_keys_str_mv | AT kudratovkh somelimittheoremsforthecriticalgaltonwatsonbranchingprocesses AT khusanbaevya somelimittheoremsforthecriticalgaltonwatsonbranchingprocesses AT kudratovkh somelimittheoremsforthecriticalgaltonwatsonbranchingprocesses AT khusanbaevya somelimittheoremsforthecriticalgaltonwatsonbranchingprocesses |